Properties

Label 39.4.e.c.16.3
Level $39$
Weight $4$
Character 39.16
Analytic conductor $2.301$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,4,Mod(16,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.3
Root \(-0.733051 - 1.26968i\) of defining polynomial
Character \(\chi\) \(=\) 39.16
Dual form 39.4.e.c.22.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.733051 + 1.26968i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.92527 - 5.06672i) q^{4} +9.85055 q^{5} +(-2.19915 + 3.80904i) q^{6} +(-14.9698 + 25.9285i) q^{7} +20.3063 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(0.733051 + 1.26968i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.92527 - 5.06672i) q^{4} +9.85055 q^{5} +(-2.19915 + 3.80904i) q^{6} +(-14.9698 + 25.9285i) q^{7} +20.3063 q^{8} +(-4.50000 + 7.79423i) q^{9} +(7.22095 + 12.5071i) q^{10} +(-23.4629 - 40.6389i) q^{11} +17.5516 q^{12} +(3.71050 - 46.7251i) q^{13} -43.8945 q^{14} +(14.7758 + 25.5925i) q^{15} +(-8.51663 - 14.7512i) q^{16} +(24.1308 - 41.7958i) q^{17} -13.1949 q^{18} +(-60.1501 + 104.183i) q^{19} +(28.8155 - 49.9100i) q^{20} -89.8188 q^{21} +(34.3990 - 59.5807i) q^{22} +(-65.3485 - 113.187i) q^{23} +(30.4595 + 52.7573i) q^{24} -27.9667 q^{25} +(62.0459 - 29.5407i) q^{26} -27.0000 q^{27} +(87.5815 + 151.696i) q^{28} +(97.4729 + 168.828i) q^{29} +(-21.6629 + 37.5212i) q^{30} -32.0123 q^{31} +(93.7115 - 162.313i) q^{32} +(70.3886 - 121.917i) q^{33} +70.7565 q^{34} +(-147.461 + 255.409i) q^{35} +(26.3275 + 45.6005i) q^{36} +(16.2125 + 28.0808i) q^{37} -176.372 q^{38} +(126.961 - 60.4474i) q^{39} +200.028 q^{40} +(120.913 + 209.427i) q^{41} +(-65.8418 - 114.041i) q^{42} +(-48.2044 + 83.4924i) q^{43} -274.541 q^{44} +(-44.3275 + 76.7774i) q^{45} +(95.8076 - 165.944i) q^{46} +539.015 q^{47} +(25.5499 - 44.2537i) q^{48} +(-276.690 - 479.241i) q^{49} +(-20.5010 - 35.5088i) q^{50} +144.785 q^{51} +(-225.889 - 155.484i) q^{52} -152.277 q^{53} +(-19.7924 - 34.2814i) q^{54} +(-231.122 - 400.315i) q^{55} +(-303.981 + 526.511i) q^{56} -360.901 q^{57} +(-142.905 + 247.519i) q^{58} +(-163.896 + 283.876i) q^{59} +172.893 q^{60} +(49.2090 - 85.2325i) q^{61} +(-23.4666 - 40.6454i) q^{62} +(-134.728 - 233.356i) q^{63} +138.515 q^{64} +(36.5504 - 460.267i) q^{65} +206.394 q^{66} +(220.575 + 382.048i) q^{67} +(-141.178 - 244.528i) q^{68} +(196.046 - 339.561i) q^{69} -432.385 q^{70} +(-172.524 + 298.821i) q^{71} +(-91.3784 + 158.272i) q^{72} +773.839 q^{73} +(-23.7691 + 41.1694i) q^{74} +(-41.9501 - 72.6597i) q^{75} +(351.911 + 609.528i) q^{76} +1404.94 q^{77} +(169.818 + 116.889i) q^{78} -150.332 q^{79} +(-83.8934 - 145.308i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-177.270 + 307.041i) q^{82} +337.966 q^{83} +(-262.745 + 455.087i) q^{84} +(237.702 - 411.711i) q^{85} -141.345 q^{86} +(-292.419 + 506.484i) q^{87} +(-476.444 - 825.226i) q^{88} +(-84.9567 - 147.149i) q^{89} -129.977 q^{90} +(1155.96 + 795.673i) q^{91} -764.649 q^{92} +(-48.0184 - 83.1703i) q^{93} +(395.125 + 684.377i) q^{94} +(-592.511 + 1026.26i) q^{95} +562.269 q^{96} +(-107.101 + 185.504i) q^{97} +(405.656 - 702.616i) q^{98} +422.332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.733051 + 1.26968i 0.259173 + 0.448900i 0.966021 0.258465i \(-0.0832168\pi\)
−0.706848 + 0.707366i \(0.749883\pi\)
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) 2.92527 5.06672i 0.365659 0.633340i
\(5\) 9.85055 0.881060 0.440530 0.897738i \(-0.354791\pi\)
0.440530 + 0.897738i \(0.354791\pi\)
\(6\) −2.19915 + 3.80904i −0.149633 + 0.259173i
\(7\) −14.9698 + 25.9285i −0.808293 + 1.40001i 0.105752 + 0.994393i \(0.466275\pi\)
−0.914045 + 0.405613i \(0.867058\pi\)
\(8\) 20.3063 0.897421
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 7.22095 + 12.5071i 0.228347 + 0.395508i
\(11\) −23.4629 40.6389i −0.643120 1.11392i −0.984732 0.174076i \(-0.944306\pi\)
0.341612 0.939841i \(-0.389027\pi\)
\(12\) 17.5516 0.422227
\(13\) 3.71050 46.7251i 0.0791621 0.996862i
\(14\) −43.8945 −0.837950
\(15\) 14.7758 + 25.5925i 0.254340 + 0.440530i
\(16\) −8.51663 14.7512i −0.133072 0.230488i
\(17\) 24.1308 41.7958i 0.344270 0.596292i −0.640951 0.767582i \(-0.721460\pi\)
0.985221 + 0.171289i \(0.0547932\pi\)
\(18\) −13.1949 −0.172782
\(19\) −60.1501 + 104.183i −0.726283 + 1.25796i 0.232161 + 0.972677i \(0.425421\pi\)
−0.958444 + 0.285282i \(0.907913\pi\)
\(20\) 28.8155 49.9100i 0.322167 0.558010i
\(21\) −89.8188 −0.933337
\(22\) 34.3990 59.5807i 0.333358 0.577393i
\(23\) −65.3485 113.187i −0.592440 1.02614i −0.993903 0.110260i \(-0.964832\pi\)
0.401463 0.915875i \(-0.368502\pi\)
\(24\) 30.4595 + 52.7573i 0.259063 + 0.448710i
\(25\) −27.9667 −0.223734
\(26\) 62.0459 29.5407i 0.468008 0.222823i
\(27\) −27.0000 −0.192450
\(28\) 87.5815 + 151.696i 0.591120 + 1.02385i
\(29\) 97.4729 + 168.828i 0.624147 + 1.08105i 0.988705 + 0.149874i \(0.0478867\pi\)
−0.364558 + 0.931181i \(0.618780\pi\)
\(30\) −21.6629 + 37.5212i −0.131836 + 0.228347i
\(31\) −32.0123 −0.185470 −0.0927351 0.995691i \(-0.529561\pi\)
−0.0927351 + 0.995691i \(0.529561\pi\)
\(32\) 93.7115 162.313i 0.517688 0.896661i
\(33\) 70.3886 121.917i 0.371306 0.643120i
\(34\) 70.7565 0.356901
\(35\) −147.461 + 255.409i −0.712155 + 1.23349i
\(36\) 26.3275 + 45.6005i 0.121886 + 0.211113i
\(37\) 16.2125 + 28.0808i 0.0720355 + 0.124769i 0.899793 0.436316i \(-0.143717\pi\)
−0.827758 + 0.561086i \(0.810384\pi\)
\(38\) −176.372 −0.752931
\(39\) 126.961 60.4474i 0.521283 0.248188i
\(40\) 200.028 0.790681
\(41\) 120.913 + 209.427i 0.460570 + 0.797731i 0.998989 0.0449461i \(-0.0143116\pi\)
−0.538419 + 0.842677i \(0.680978\pi\)
\(42\) −65.8418 114.041i −0.241895 0.418975i
\(43\) −48.2044 + 83.4924i −0.170956 + 0.296104i −0.938754 0.344587i \(-0.888019\pi\)
0.767799 + 0.640691i \(0.221352\pi\)
\(44\) −274.541 −0.940651
\(45\) −44.3275 + 76.7774i −0.146843 + 0.254340i
\(46\) 95.8076 165.944i 0.307088 0.531892i
\(47\) 539.015 1.67284 0.836419 0.548090i \(-0.184645\pi\)
0.836419 + 0.548090i \(0.184645\pi\)
\(48\) 25.5499 44.2537i 0.0768293 0.133072i
\(49\) −276.690 479.241i −0.806676 1.39720i
\(50\) −20.5010 35.5088i −0.0579857 0.100434i
\(51\) 144.785 0.397528
\(52\) −225.889 155.484i −0.602406 0.414648i
\(53\) −152.277 −0.394657 −0.197328 0.980337i \(-0.563226\pi\)
−0.197328 + 0.980337i \(0.563226\pi\)
\(54\) −19.7924 34.2814i −0.0498778 0.0863909i
\(55\) −231.122 400.315i −0.566627 0.981427i
\(56\) −303.981 + 526.511i −0.725379 + 1.25639i
\(57\) −360.901 −0.838640
\(58\) −142.905 + 247.519i −0.323524 + 0.560359i
\(59\) −163.896 + 283.876i −0.361652 + 0.626399i −0.988233 0.152957i \(-0.951120\pi\)
0.626581 + 0.779356i \(0.284454\pi\)
\(60\) 172.893 0.372007
\(61\) 49.2090 85.2325i 0.103288 0.178900i −0.809749 0.586776i \(-0.800397\pi\)
0.913037 + 0.407876i \(0.133730\pi\)
\(62\) −23.4666 40.6454i −0.0480688 0.0832576i
\(63\) −134.728 233.356i −0.269431 0.466668i
\(64\) 138.515 0.270537
\(65\) 36.5504 460.267i 0.0697465 0.878295i
\(66\) 206.394 0.384929
\(67\) 220.575 + 382.048i 0.402202 + 0.696635i 0.993991 0.109458i \(-0.0349115\pi\)
−0.591789 + 0.806093i \(0.701578\pi\)
\(68\) −141.178 244.528i −0.251771 0.436080i
\(69\) 196.046 339.561i 0.342045 0.592440i
\(70\) −432.385 −0.738284
\(71\) −172.524 + 298.821i −0.288379 + 0.499486i −0.973423 0.229015i \(-0.926449\pi\)
0.685044 + 0.728501i \(0.259783\pi\)
\(72\) −91.3784 + 158.272i −0.149570 + 0.259063i
\(73\) 773.839 1.24070 0.620349 0.784326i \(-0.286991\pi\)
0.620349 + 0.784326i \(0.286991\pi\)
\(74\) −23.7691 + 41.1694i −0.0373393 + 0.0646735i
\(75\) −41.9501 72.6597i −0.0645864 0.111867i
\(76\) 351.911 + 609.528i 0.531144 + 0.919969i
\(77\) 1404.94 2.07932
\(78\) 169.818 + 116.889i 0.246514 + 0.169680i
\(79\) −150.332 −0.214097 −0.107049 0.994254i \(-0.534140\pi\)
−0.107049 + 0.994254i \(0.534140\pi\)
\(80\) −83.8934 145.308i −0.117245 0.203074i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −177.270 + 307.041i −0.238734 + 0.413500i
\(83\) 337.966 0.446947 0.223473 0.974710i \(-0.428260\pi\)
0.223473 + 0.974710i \(0.428260\pi\)
\(84\) −262.745 + 455.087i −0.341283 + 0.591120i
\(85\) 237.702 411.711i 0.303322 0.525369i
\(86\) −141.345 −0.177228
\(87\) −292.419 + 506.484i −0.360351 + 0.624147i
\(88\) −476.444 825.226i −0.577149 0.999652i
\(89\) −84.9567 147.149i −0.101184 0.175256i 0.810989 0.585062i \(-0.198930\pi\)
−0.912173 + 0.409806i \(0.865596\pi\)
\(90\) −129.977 −0.152231
\(91\) 1155.96 + 795.673i 1.33163 + 0.916584i
\(92\) −764.649 −0.866524
\(93\) −48.0184 83.1703i −0.0535406 0.0927351i
\(94\) 395.125 + 684.377i 0.433554 + 0.750937i
\(95\) −592.511 + 1026.26i −0.639899 + 1.10834i
\(96\) 562.269 0.597774
\(97\) −107.101 + 185.504i −0.112107 + 0.194176i −0.916620 0.399760i \(-0.869093\pi\)
0.804512 + 0.593936i \(0.202427\pi\)
\(98\) 405.656 702.616i 0.418137 0.724234i
\(99\) 422.332 0.428747
\(100\) −81.8104 + 141.700i −0.0818104 + 0.141700i
\(101\) −797.556 1381.41i −0.785741 1.36094i −0.928555 0.371194i \(-0.878949\pi\)
0.142815 0.989749i \(-0.454385\pi\)
\(102\) 106.135 + 183.831i 0.103028 + 0.178450i
\(103\) −1570.30 −1.50219 −0.751096 0.660193i \(-0.770475\pi\)
−0.751096 + 0.660193i \(0.770475\pi\)
\(104\) 75.3465 948.814i 0.0710417 0.894604i
\(105\) −884.764 −0.822325
\(106\) −111.626 193.343i −0.102284 0.177161i
\(107\) 3.36651 + 5.83096i 0.00304161 + 0.00526823i 0.867542 0.497364i \(-0.165698\pi\)
−0.864501 + 0.502632i \(0.832365\pi\)
\(108\) −78.9824 + 136.801i −0.0703711 + 0.121886i
\(109\) −542.422 −0.476648 −0.238324 0.971186i \(-0.576598\pi\)
−0.238324 + 0.971186i \(0.576598\pi\)
\(110\) 338.848 586.903i 0.293708 0.508718i
\(111\) −48.6374 + 84.2425i −0.0415897 + 0.0720355i
\(112\) 509.969 0.430246
\(113\) 721.411 1249.52i 0.600572 1.04022i −0.392162 0.919896i \(-0.628273\pi\)
0.992735 0.120325i \(-0.0383938\pi\)
\(114\) −264.558 458.229i −0.217352 0.376465i
\(115\) −643.719 1114.95i −0.521975 0.904087i
\(116\) 1140.54 0.912900
\(117\) 347.489 + 239.183i 0.274576 + 0.188996i
\(118\) −480.577 −0.374921
\(119\) 722.467 + 1251.35i 0.556542 + 0.963958i
\(120\) 300.042 + 519.689i 0.228250 + 0.395340i
\(121\) −435.513 + 754.330i −0.327207 + 0.566739i
\(122\) 144.291 0.107078
\(123\) −362.738 + 628.280i −0.265910 + 0.460570i
\(124\) −93.6446 + 162.197i −0.0678188 + 0.117466i
\(125\) −1506.81 −1.07818
\(126\) 197.525 342.124i 0.139658 0.241895i
\(127\) 1246.42 + 2158.86i 0.870881 + 1.50841i 0.861087 + 0.508458i \(0.169784\pi\)
0.00979442 + 0.999952i \(0.496882\pi\)
\(128\) −648.153 1122.63i −0.447572 0.775217i
\(129\) −289.226 −0.197403
\(130\) 611.186 290.992i 0.412343 0.196321i
\(131\) 744.561 0.496585 0.248292 0.968685i \(-0.420131\pi\)
0.248292 + 0.968685i \(0.420131\pi\)
\(132\) −411.812 713.279i −0.271543 0.470326i
\(133\) −1800.87 3119.20i −1.17410 2.03360i
\(134\) −323.386 + 560.121i −0.208480 + 0.361097i
\(135\) −265.965 −0.169560
\(136\) 490.008 848.718i 0.308955 0.535125i
\(137\) 111.083 192.402i 0.0692736 0.119985i −0.829308 0.558792i \(-0.811265\pi\)
0.898582 + 0.438806i \(0.144599\pi\)
\(138\) 574.846 0.354595
\(139\) 388.573 673.028i 0.237110 0.410687i −0.722774 0.691085i \(-0.757133\pi\)
0.959884 + 0.280398i \(0.0904665\pi\)
\(140\) 862.726 + 1494.28i 0.520812 + 0.902072i
\(141\) 808.522 + 1400.40i 0.482907 + 0.836419i
\(142\) −505.876 −0.298959
\(143\) −1985.91 + 945.514i −1.16133 + 0.552922i
\(144\) 153.299 0.0887149
\(145\) 960.161 + 1663.05i 0.549911 + 0.952473i
\(146\) 567.263 + 982.529i 0.321555 + 0.556950i
\(147\) 830.070 1437.72i 0.465735 0.806676i
\(148\) 189.704 0.105362
\(149\) −889.147 + 1540.05i −0.488871 + 0.846750i −0.999918 0.0128032i \(-0.995925\pi\)
0.511047 + 0.859553i \(0.329258\pi\)
\(150\) 61.5031 106.527i 0.0334781 0.0579857i
\(151\) 1166.00 0.628394 0.314197 0.949358i \(-0.398265\pi\)
0.314197 + 0.949358i \(0.398265\pi\)
\(152\) −1221.43 + 2115.57i −0.651781 + 1.12892i
\(153\) 217.177 + 376.162i 0.114757 + 0.198764i
\(154\) 1029.89 + 1783.82i 0.538902 + 0.933407i
\(155\) −315.338 −0.163410
\(156\) 65.1253 820.102i 0.0334244 0.420902i
\(157\) 517.628 0.263129 0.131564 0.991308i \(-0.458000\pi\)
0.131564 + 0.991308i \(0.458000\pi\)
\(158\) −110.201 190.874i −0.0554882 0.0961083i
\(159\) −228.415 395.626i −0.113928 0.197328i
\(160\) 923.109 1598.87i 0.456114 0.790012i
\(161\) 3913.02 1.91546
\(162\) 59.3771 102.844i 0.0287970 0.0498778i
\(163\) −305.094 + 528.438i −0.146606 + 0.253929i −0.929971 0.367633i \(-0.880168\pi\)
0.783365 + 0.621562i \(0.213502\pi\)
\(164\) 1414.81 0.673647
\(165\) 693.366 1200.95i 0.327142 0.566627i
\(166\) 247.746 + 429.109i 0.115836 + 0.200635i
\(167\) −1491.51 2583.36i −0.691115 1.19705i −0.971473 0.237150i \(-0.923787\pi\)
0.280358 0.959895i \(-0.409547\pi\)
\(168\) −1823.89 −0.837596
\(169\) −2169.46 346.747i −0.987467 0.157827i
\(170\) 696.990 0.314451
\(171\) −541.351 937.647i −0.242094 0.419320i
\(172\) 282.022 + 488.476i 0.125023 + 0.216546i
\(173\) −489.106 + 847.157i −0.214948 + 0.372301i −0.953257 0.302162i \(-0.902292\pi\)
0.738308 + 0.674463i \(0.235625\pi\)
\(174\) −857.431 −0.373573
\(175\) 418.657 725.134i 0.180843 0.313229i
\(176\) −399.649 + 692.213i −0.171163 + 0.296463i
\(177\) −983.377 −0.417599
\(178\) 124.555 215.736i 0.0524483 0.0908431i
\(179\) −926.471 1604.69i −0.386858 0.670058i 0.605167 0.796099i \(-0.293106\pi\)
−0.992025 + 0.126040i \(0.959773\pi\)
\(180\) 259.340 + 449.190i 0.107389 + 0.186003i
\(181\) 852.777 0.350201 0.175101 0.984551i \(-0.443975\pi\)
0.175101 + 0.984551i \(0.443975\pi\)
\(182\) −162.871 + 2050.97i −0.0663339 + 0.835320i
\(183\) 295.254 0.119267
\(184\) −1326.99 2298.41i −0.531668 0.920875i
\(185\) 159.702 + 276.612i 0.0634676 + 0.109929i
\(186\) 70.3999 121.936i 0.0277525 0.0480688i
\(187\) −2264.71 −0.885627
\(188\) 1576.77 2731.04i 0.611689 1.05948i
\(189\) 404.185 700.068i 0.155556 0.269431i
\(190\) −1737.36 −0.663377
\(191\) −2220.65 + 3846.27i −0.841258 + 1.45710i 0.0475730 + 0.998868i \(0.484851\pi\)
−0.888831 + 0.458234i \(0.848482\pi\)
\(192\) 207.773 + 359.873i 0.0780974 + 0.135269i
\(193\) 1241.21 + 2149.85i 0.462925 + 0.801810i 0.999105 0.0422935i \(-0.0134665\pi\)
−0.536180 + 0.844104i \(0.680133\pi\)
\(194\) −314.041 −0.116221
\(195\) 1250.64 595.440i 0.459281 0.218669i
\(196\) −3237.57 −1.17987
\(197\) −630.115 1091.39i −0.227888 0.394713i 0.729294 0.684200i \(-0.239849\pi\)
−0.957182 + 0.289487i \(0.906515\pi\)
\(198\) 309.591 + 536.227i 0.111119 + 0.192464i
\(199\) 2760.48 4781.30i 0.983344 1.70320i 0.334266 0.942479i \(-0.391511\pi\)
0.649077 0.760722i \(-0.275155\pi\)
\(200\) −567.901 −0.200783
\(201\) −661.726 + 1146.14i −0.232212 + 0.402202i
\(202\) 1169.30 2025.28i 0.407285 0.705438i
\(203\) −5836.60 −2.01798
\(204\) 423.535 733.585i 0.145360 0.251771i
\(205\) 1191.06 + 2062.97i 0.405790 + 0.702849i
\(206\) −1151.11 1993.78i −0.389327 0.674334i
\(207\) 1176.27 0.394960
\(208\) −720.853 + 343.206i −0.240299 + 0.114409i
\(209\) 5645.18 1.86835
\(210\) −648.577 1123.37i −0.213124 0.369142i
\(211\) 2263.90 + 3921.18i 0.738640 + 1.27936i 0.953108 + 0.302631i \(0.0978649\pi\)
−0.214468 + 0.976731i \(0.568802\pi\)
\(212\) −445.451 + 771.543i −0.144310 + 0.249952i
\(213\) −1035.15 −0.332991
\(214\) −4.93564 + 8.54879i −0.00157661 + 0.00273076i
\(215\) −474.839 + 822.446i −0.150622 + 0.260885i
\(216\) −548.270 −0.172709
\(217\) 479.217 830.029i 0.149914 0.259659i
\(218\) −397.623 688.703i −0.123534 0.213967i
\(219\) 1160.76 + 2010.49i 0.358159 + 0.620349i
\(220\) −2704.38 −0.828770
\(221\) −1863.37 1282.60i −0.567168 0.390393i
\(222\) −142.615 −0.0431157
\(223\) −2240.59 3880.81i −0.672829 1.16537i −0.977099 0.212787i \(-0.931746\pi\)
0.304270 0.952586i \(-0.401588\pi\)
\(224\) 2805.68 + 4859.59i 0.836887 + 1.44953i
\(225\) 125.850 217.979i 0.0372890 0.0645864i
\(226\) 2115.32 0.622607
\(227\) 2879.88 4988.09i 0.842044 1.45846i −0.0461191 0.998936i \(-0.514685\pi\)
0.888163 0.459528i \(-0.151981\pi\)
\(228\) −1055.73 + 1828.58i −0.306656 + 0.531144i
\(229\) −4635.08 −1.33753 −0.668766 0.743473i \(-0.733177\pi\)
−0.668766 + 0.743473i \(0.733177\pi\)
\(230\) 943.757 1634.64i 0.270563 0.468629i
\(231\) 2107.41 + 3650.14i 0.600248 + 1.03966i
\(232\) 1979.31 + 3428.27i 0.560122 + 0.970160i
\(233\) 5886.33 1.65505 0.827524 0.561431i \(-0.189749\pi\)
0.827524 + 0.561431i \(0.189749\pi\)
\(234\) −48.9597 + 616.533i −0.0136778 + 0.172240i
\(235\) 5309.59 1.47387
\(236\) 958.882 + 1660.83i 0.264483 + 0.458097i
\(237\) −225.498 390.574i −0.0618046 0.107049i
\(238\) −1059.21 + 1834.61i −0.288481 + 0.499663i
\(239\) 2135.84 0.578060 0.289030 0.957320i \(-0.406667\pi\)
0.289030 + 0.957320i \(0.406667\pi\)
\(240\) 251.680 435.923i 0.0676912 0.117245i
\(241\) −2346.46 + 4064.19i −0.627173 + 1.08630i 0.360943 + 0.932588i \(0.382455\pi\)
−0.988116 + 0.153708i \(0.950879\pi\)
\(242\) −1277.01 −0.339212
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −287.899 498.656i −0.0755364 0.130833i
\(245\) −2725.55 4720.79i −0.710730 1.23102i
\(246\) −1063.62 −0.275667
\(247\) 4644.77 + 3197.09i 1.19652 + 0.823587i
\(248\) −650.051 −0.166445
\(249\) 506.949 + 878.062i 0.129022 + 0.223473i
\(250\) −1104.57 1913.16i −0.279435 0.483996i
\(251\) 1951.44 3379.99i 0.490732 0.849973i −0.509211 0.860642i \(-0.670063\pi\)
0.999943 + 0.0106687i \(0.00339603\pi\)
\(252\) −1576.47 −0.394080
\(253\) −3066.53 + 5311.38i −0.762020 + 1.31986i
\(254\) −1827.38 + 3165.11i −0.451417 + 0.781877i
\(255\) 1426.21 0.350246
\(256\) 1504.32 2605.56i 0.367265 0.636122i
\(257\) 2065.42 + 3577.40i 0.501312 + 0.868297i 0.999999 + 0.00151510i \(0.000482272\pi\)
−0.498687 + 0.866782i \(0.666184\pi\)
\(258\) −212.017 367.225i −0.0511614 0.0886141i
\(259\) −970.790 −0.232903
\(260\) −2225.13 1531.60i −0.530756 0.365330i
\(261\) −1754.51 −0.416098
\(262\) 545.801 + 945.356i 0.128701 + 0.222917i
\(263\) −3176.09 5501.14i −0.744661 1.28979i −0.950353 0.311174i \(-0.899278\pi\)
0.205692 0.978617i \(-0.434056\pi\)
\(264\) 1429.33 2475.68i 0.333217 0.577149i
\(265\) −1500.01 −0.347716
\(266\) 2640.26 4573.06i 0.608589 1.05411i
\(267\) 254.870 441.448i 0.0584187 0.101184i
\(268\) 2580.97 0.588276
\(269\) −90.7619 + 157.204i −0.0205719 + 0.0356316i −0.876128 0.482078i \(-0.839882\pi\)
0.855556 + 0.517710i \(0.173215\pi\)
\(270\) −194.966 337.690i −0.0439453 0.0761155i
\(271\) −1730.18 2996.75i −0.387825 0.671733i 0.604331 0.796733i \(-0.293440\pi\)
−0.992157 + 0.125000i \(0.960107\pi\)
\(272\) −822.053 −0.183251
\(273\) −333.273 + 4196.79i −0.0738849 + 0.930408i
\(274\) 325.719 0.0718153
\(275\) 656.180 + 1136.54i 0.143888 + 0.249221i
\(276\) −1146.97 1986.62i −0.250144 0.433262i
\(277\) 3218.97 5575.42i 0.698228 1.20937i −0.270853 0.962621i \(-0.587306\pi\)
0.969080 0.246745i \(-0.0793611\pi\)
\(278\) 1139.37 0.245810
\(279\) 144.055 249.511i 0.0309117 0.0535406i
\(280\) −2994.38 + 5186.42i −0.639102 + 1.10696i
\(281\) −2974.26 −0.631421 −0.315711 0.948855i \(-0.602243\pi\)
−0.315711 + 0.948855i \(0.602243\pi\)
\(282\) −1185.38 + 2053.13i −0.250312 + 0.433554i
\(283\) −1517.86 2629.01i −0.318825 0.552221i 0.661418 0.750017i \(-0.269955\pi\)
−0.980243 + 0.197797i \(0.936621\pi\)
\(284\) 1009.36 + 1748.27i 0.210896 + 0.365283i
\(285\) −3555.07 −0.738891
\(286\) −2656.28 1828.37i −0.549192 0.378020i
\(287\) −7240.15 −1.48910
\(288\) 843.403 + 1460.82i 0.172563 + 0.298887i
\(289\) 1291.91 + 2237.65i 0.262957 + 0.455455i
\(290\) −1407.69 + 2438.20i −0.285044 + 0.493710i
\(291\) −642.604 −0.129451
\(292\) 2263.69 3920.83i 0.453673 0.785784i
\(293\) 977.872 1693.72i 0.194976 0.337708i −0.751917 0.659258i \(-0.770871\pi\)
0.946893 + 0.321550i \(0.104204\pi\)
\(294\) 2433.93 0.482823
\(295\) −1614.47 + 2796.34i −0.318637 + 0.551895i
\(296\) 329.216 + 570.218i 0.0646462 + 0.111970i
\(297\) 633.498 + 1097.25i 0.123769 + 0.214373i
\(298\) −2607.16 −0.506808
\(299\) −5531.15 + 2633.43i −1.06981 + 0.509349i
\(300\) −490.862 −0.0944665
\(301\) −1443.22 2499.73i −0.276365 0.478678i
\(302\) 854.736 + 1480.45i 0.162863 + 0.282086i
\(303\) 2392.67 4144.22i 0.453648 0.785741i
\(304\) 2049.10 0.386593
\(305\) 484.735 839.586i 0.0910029 0.157622i
\(306\) −318.404 + 551.492i −0.0594835 + 0.103028i
\(307\) −1027.56 −0.191029 −0.0955147 0.995428i \(-0.530450\pi\)
−0.0955147 + 0.995428i \(0.530450\pi\)
\(308\) 4109.83 7118.43i 0.760322 1.31692i
\(309\) −2355.44 4079.75i −0.433646 0.751096i
\(310\) −231.159 400.379i −0.0423515 0.0733549i
\(311\) 3405.61 0.620947 0.310474 0.950582i \(-0.399512\pi\)
0.310474 + 0.950582i \(0.399512\pi\)
\(312\) 2578.11 1227.46i 0.467810 0.222729i
\(313\) 4813.20 0.869196 0.434598 0.900625i \(-0.356890\pi\)
0.434598 + 0.900625i \(0.356890\pi\)
\(314\) 379.447 + 657.222i 0.0681957 + 0.118118i
\(315\) −1327.15 2298.69i −0.237385 0.411163i
\(316\) −439.763 + 761.691i −0.0782866 + 0.135596i
\(317\) 1141.33 0.202219 0.101110 0.994875i \(-0.467761\pi\)
0.101110 + 0.994875i \(0.467761\pi\)
\(318\) 334.879 580.028i 0.0590538 0.102284i
\(319\) 4573.99 7922.38i 0.802803 1.39050i
\(320\) 1364.45 0.238359
\(321\) −10.0995 + 17.4929i −0.00175608 + 0.00304161i
\(322\) 2868.44 + 4968.29i 0.496435 + 0.859850i
\(323\) 2902.94 + 5028.04i 0.500074 + 0.866154i
\(324\) −473.894 −0.0812576
\(325\) −103.771 + 1306.75i −0.0177113 + 0.223032i
\(326\) −894.597 −0.151985
\(327\) −813.633 1409.25i −0.137596 0.238324i
\(328\) 2455.29 + 4252.69i 0.413325 + 0.715900i
\(329\) −8068.94 + 13975.8i −1.35214 + 2.34198i
\(330\) 2033.09 0.339145
\(331\) −3826.28 + 6627.32i −0.635382 + 1.10051i 0.351052 + 0.936356i \(0.385824\pi\)
−0.986434 + 0.164158i \(0.947509\pi\)
\(332\) 988.643 1712.38i 0.163430 0.283069i
\(333\) −291.825 −0.0480237
\(334\) 2186.70 3787.47i 0.358236 0.620483i
\(335\) 2172.79 + 3763.38i 0.354364 + 0.613777i
\(336\) 764.953 + 1324.94i 0.124201 + 0.215123i
\(337\) −2503.69 −0.404702 −0.202351 0.979313i \(-0.564858\pi\)
−0.202351 + 0.979313i \(0.564858\pi\)
\(338\) −1150.07 3008.71i −0.185076 0.484178i
\(339\) 4328.47 0.693481
\(340\) −1390.68 2408.74i −0.221825 0.384212i
\(341\) 751.100 + 1300.94i 0.119280 + 0.206598i
\(342\) 793.675 1374.69i 0.125488 0.217352i
\(343\) 6298.69 0.991537
\(344\) −978.853 + 1695.42i −0.153419 + 0.265730i
\(345\) 1931.16 3344.86i 0.301362 0.521975i
\(346\) −1434.16 −0.222835
\(347\) −2248.06 + 3893.75i −0.347787 + 0.602385i −0.985856 0.167594i \(-0.946400\pi\)
0.638069 + 0.769979i \(0.279733\pi\)
\(348\) 1710.81 + 2963.21i 0.263532 + 0.456450i
\(349\) −1788.81 3098.31i −0.274363 0.475211i 0.695611 0.718418i \(-0.255134\pi\)
−0.969974 + 0.243208i \(0.921800\pi\)
\(350\) 1227.59 0.187478
\(351\) −100.183 + 1261.58i −0.0152348 + 0.191846i
\(352\) −8794.96 −1.33174
\(353\) 4022.58 + 6967.32i 0.606517 + 1.05052i 0.991810 + 0.127724i \(0.0407672\pi\)
−0.385293 + 0.922794i \(0.625900\pi\)
\(354\) −720.865 1248.57i −0.108230 0.187460i
\(355\) −1699.46 + 2943.55i −0.254079 + 0.440077i
\(356\) −994.086 −0.147996
\(357\) −2167.40 + 3754.05i −0.321319 + 0.556542i
\(358\) 1358.30 2352.64i 0.200526 0.347322i
\(359\) −2172.90 −0.319447 −0.159724 0.987162i \(-0.551060\pi\)
−0.159724 + 0.987162i \(0.551060\pi\)
\(360\) −900.127 + 1559.07i −0.131780 + 0.228250i
\(361\) −3806.57 6593.17i −0.554974 0.961244i
\(362\) 625.129 + 1082.75i 0.0907625 + 0.157205i
\(363\) −2613.08 −0.377826
\(364\) 7412.96 3529.39i 1.06743 0.508215i
\(365\) 7622.74 1.09313
\(366\) 216.436 + 374.878i 0.0309107 + 0.0535388i
\(367\) −3831.38 6636.15i −0.544949 0.943880i −0.998610 0.0527056i \(-0.983216\pi\)
0.453661 0.891175i \(-0.350118\pi\)
\(368\) −1113.10 + 1927.94i −0.157675 + 0.273100i
\(369\) −2176.43 −0.307047
\(370\) −234.139 + 405.541i −0.0328981 + 0.0569812i
\(371\) 2279.55 3948.30i 0.318998 0.552521i
\(372\) −561.868 −0.0783105
\(373\) −5271.27 + 9130.10i −0.731732 + 1.26740i 0.224411 + 0.974495i \(0.427954\pi\)
−0.956143 + 0.292902i \(0.905379\pi\)
\(374\) −1660.15 2875.46i −0.229530 0.397558i
\(375\) −2260.21 3914.80i −0.311244 0.539091i
\(376\) 10945.4 1.50124
\(377\) 8250.17 3927.99i 1.12707 0.536610i
\(378\) 1185.15 0.161264
\(379\) −2737.77 4741.96i −0.371055 0.642686i 0.618673 0.785648i \(-0.287671\pi\)
−0.989728 + 0.142962i \(0.954337\pi\)
\(380\) 3466.51 + 6004.18i 0.467970 + 0.810547i
\(381\) −3739.26 + 6476.59i −0.502803 + 0.870881i
\(382\) −6511.39 −0.872124
\(383\) −404.042 + 699.822i −0.0539050 + 0.0933661i −0.891719 0.452590i \(-0.850500\pi\)
0.837814 + 0.545956i \(0.183833\pi\)
\(384\) 1944.46 3367.90i 0.258406 0.447572i
\(385\) 13839.4 1.83200
\(386\) −1819.75 + 3151.89i −0.239955 + 0.415614i
\(387\) −433.839 751.432i −0.0569852 0.0987013i
\(388\) 626.597 + 1085.30i 0.0819862 + 0.142004i
\(389\) −7060.26 −0.920230 −0.460115 0.887859i \(-0.652192\pi\)
−0.460115 + 0.887859i \(0.652192\pi\)
\(390\) 1672.80 + 1151.42i 0.217193 + 0.149499i
\(391\) −6307.65 −0.815836
\(392\) −5618.55 9731.62i −0.723928 1.25388i
\(393\) 1116.84 + 1934.43i 0.143352 + 0.248292i
\(394\) 923.813 1600.09i 0.118124 0.204598i
\(395\) −1480.85 −0.188633
\(396\) 1235.44 2139.84i 0.156775 0.271543i
\(397\) 709.947 1229.66i 0.0897511 0.155453i −0.817655 0.575709i \(-0.804726\pi\)
0.907406 + 0.420255i \(0.138060\pi\)
\(398\) 8094.29 1.01942
\(399\) 5402.61 9357.60i 0.677867 1.17410i
\(400\) 238.182 + 412.544i 0.0297728 + 0.0515680i
\(401\) −5335.37 9241.13i −0.664428 1.15082i −0.979440 0.201735i \(-0.935342\pi\)
0.315012 0.949088i \(-0.397991\pi\)
\(402\) −1940.31 −0.240732
\(403\) −118.782 + 1495.78i −0.0146822 + 0.184888i
\(404\) −9332.28 −1.14925
\(405\) −398.947 690.997i −0.0489478 0.0847800i
\(406\) −4278.52 7410.62i −0.523004 0.905869i
\(407\) 760.782 1317.71i 0.0926550 0.160483i
\(408\) 2940.05 0.356750
\(409\) −3175.78 + 5500.61i −0.383942 + 0.665007i −0.991622 0.129175i \(-0.958767\pi\)
0.607680 + 0.794182i \(0.292100\pi\)
\(410\) −1746.21 + 3024.52i −0.210339 + 0.364318i
\(411\) 666.500 0.0799903
\(412\) −4593.54 + 7956.25i −0.549290 + 0.951399i
\(413\) −4906.98 8499.15i −0.584641 1.01263i
\(414\) 862.268 + 1493.49i 0.102363 + 0.177297i
\(415\) 3329.15 0.393787
\(416\) −7236.37 4980.94i −0.852866 0.587045i
\(417\) 2331.44 0.273791
\(418\) 4138.20 + 7167.57i 0.484225 + 0.838702i
\(419\) −2808.94 4865.22i −0.327507 0.567259i 0.654509 0.756054i \(-0.272875\pi\)
−0.982017 + 0.188795i \(0.939542\pi\)
\(420\) −2588.18 + 4482.85i −0.300691 + 0.520812i
\(421\) −1518.29 −0.175765 −0.0878825 0.996131i \(-0.528010\pi\)
−0.0878825 + 0.996131i \(0.528010\pi\)
\(422\) −3319.10 + 5748.85i −0.382870 + 0.663151i
\(423\) −2425.57 + 4201.20i −0.278806 + 0.482907i
\(424\) −3092.17 −0.354173
\(425\) −674.860 + 1168.89i −0.0770248 + 0.133411i
\(426\) −758.815 1314.31i −0.0863021 0.149480i
\(427\) 1473.30 + 2551.83i 0.166974 + 0.289207i
\(428\) 39.3918 0.00444878
\(429\) −5435.39 3741.28i −0.611709 0.421051i
\(430\) −1392.33 −0.156149
\(431\) 2485.07 + 4304.26i 0.277730 + 0.481042i 0.970820 0.239809i \(-0.0770848\pi\)
−0.693091 + 0.720850i \(0.743751\pi\)
\(432\) 229.949 + 398.283i 0.0256098 + 0.0443574i
\(433\) 1649.36 2856.77i 0.183055 0.317061i −0.759864 0.650082i \(-0.774735\pi\)
0.942919 + 0.333021i \(0.108068\pi\)
\(434\) 1405.16 0.155415
\(435\) −2880.48 + 4989.14i −0.317491 + 0.549911i
\(436\) −1586.73 + 2748.30i −0.174291 + 0.301880i
\(437\) 15722.9 1.72112
\(438\) −1701.79 + 2947.59i −0.185650 + 0.321555i
\(439\) 3024.24 + 5238.13i 0.328790 + 0.569481i 0.982272 0.187461i \(-0.0600257\pi\)
−0.653482 + 0.756942i \(0.726692\pi\)
\(440\) −4693.24 8128.92i −0.508503 0.880753i
\(441\) 4980.42 0.537784
\(442\) 262.542 3306.10i 0.0282530 0.355781i
\(443\) 6822.62 0.731722 0.365861 0.930670i \(-0.380775\pi\)
0.365861 + 0.930670i \(0.380775\pi\)
\(444\) 284.555 + 492.865i 0.0304153 + 0.0526809i
\(445\) −836.869 1449.50i −0.0891493 0.154411i
\(446\) 3284.93 5689.66i 0.348757 0.604066i
\(447\) −5334.88 −0.564500
\(448\) −2073.54 + 3591.48i −0.218673 + 0.378753i
\(449\) −205.205 + 355.426i −0.0215684 + 0.0373576i −0.876608 0.481205i \(-0.840199\pi\)
0.855040 + 0.518563i \(0.173533\pi\)
\(450\) 369.019 0.0386571
\(451\) 5673.91 9827.51i 0.592404 1.02607i
\(452\) −4220.65 7310.38i −0.439209 0.760733i
\(453\) 1749.00 + 3029.35i 0.181402 + 0.314197i
\(454\) 8444.38 0.872939
\(455\) 11386.9 + 7837.81i 1.17324 + 0.807565i
\(456\) −7328.56 −0.752612
\(457\) 8321.41 + 14413.1i 0.851771 + 1.47531i 0.879609 + 0.475697i \(0.157804\pi\)
−0.0278385 + 0.999612i \(0.508862\pi\)
\(458\) −3397.75 5885.07i −0.346651 0.600418i
\(459\) −651.532 + 1128.49i −0.0662547 + 0.114757i
\(460\) −7532.21 −0.763459
\(461\) 5864.85 10158.2i 0.592523 1.02628i −0.401368 0.915917i \(-0.631465\pi\)
0.993891 0.110364i \(-0.0352015\pi\)
\(462\) −3089.67 + 5351.47i −0.311136 + 0.538902i
\(463\) −3564.93 −0.357832 −0.178916 0.983864i \(-0.557259\pi\)
−0.178916 + 0.983864i \(0.557259\pi\)
\(464\) 1660.28 2875.69i 0.166113 0.287717i
\(465\) −473.008 819.273i −0.0471725 0.0817051i
\(466\) 4314.98 + 7473.76i 0.428943 + 0.742951i
\(467\) 1134.81 0.112447 0.0562233 0.998418i \(-0.482094\pi\)
0.0562233 + 0.998418i \(0.482094\pi\)
\(468\) 2228.37 1060.95i 0.220100 0.104792i
\(469\) −13207.9 −1.30039
\(470\) 3892.20 + 6741.49i 0.381987 + 0.661620i
\(471\) 776.441 + 1344.84i 0.0759587 + 0.131564i
\(472\) −3328.12 + 5764.48i −0.324554 + 0.562144i
\(473\) 4524.05 0.439780
\(474\) 330.603 572.622i 0.0320361 0.0554882i
\(475\) 1682.20 2913.66i 0.162494 0.281448i
\(476\) 8453.65 0.814018
\(477\) 685.245 1186.88i 0.0657761 0.113928i
\(478\) 1565.68 + 2711.84i 0.149817 + 0.259491i
\(479\) 9686.30 + 16777.2i 0.923963 + 1.60035i 0.793220 + 0.608935i \(0.208403\pi\)
0.130743 + 0.991416i \(0.458264\pi\)
\(480\) 5538.66 0.526675
\(481\) 1372.24 653.335i 0.130080 0.0619325i
\(482\) −6880.29 −0.650184
\(483\) 5869.53 + 10166.3i 0.552946 + 0.957730i
\(484\) 2547.99 + 4413.24i 0.239293 + 0.414467i
\(485\) −1055.00 + 1827.31i −0.0987733 + 0.171080i
\(486\) 356.263 0.0332519
\(487\) 4522.98 7834.02i 0.420853 0.728939i −0.575170 0.818034i \(-0.695064\pi\)
0.996023 + 0.0890946i \(0.0283973\pi\)
\(488\) 999.253 1730.76i 0.0926927 0.160549i
\(489\) −1830.56 −0.169286
\(490\) 3995.93 6921.15i 0.368403 0.638093i
\(491\) −7201.66 12473.6i −0.661927 1.14649i −0.980109 0.198462i \(-0.936405\pi\)
0.318181 0.948030i \(-0.396928\pi\)
\(492\) 2122.21 + 3675.78i 0.194465 + 0.336823i
\(493\) 9408.40 0.859499
\(494\) −654.429 + 8241.01i −0.0596036 + 0.750568i
\(495\) 4160.20 0.377751
\(496\) 272.637 + 472.221i 0.0246809 + 0.0427486i
\(497\) −5165.31 8946.58i −0.466189 0.807463i
\(498\) −743.239 + 1287.33i −0.0668782 + 0.115836i
\(499\) −9319.75 −0.836091 −0.418045 0.908426i \(-0.637285\pi\)
−0.418045 + 0.908426i \(0.637285\pi\)
\(500\) −4407.82 + 7634.57i −0.394247 + 0.682856i
\(501\) 4474.52 7750.09i 0.399015 0.691115i
\(502\) 5722.02 0.508737
\(503\) −1372.99 + 2378.09i −0.121707 + 0.210802i −0.920441 0.390882i \(-0.872170\pi\)
0.798734 + 0.601684i \(0.205503\pi\)
\(504\) −2735.83 4738.60i −0.241793 0.418798i
\(505\) −7856.37 13607.6i −0.692285 1.19907i
\(506\) −8991.69 −0.789979
\(507\) −2353.32 6156.55i −0.206143 0.539294i
\(508\) 14584.5 1.27378
\(509\) 591.055 + 1023.74i 0.0514697 + 0.0891481i 0.890612 0.454763i \(-0.150276\pi\)
−0.839143 + 0.543911i \(0.816943\pi\)
\(510\) 1045.48 + 1810.83i 0.0907742 + 0.157226i
\(511\) −11584.2 + 20064.5i −1.00285 + 1.73698i
\(512\) −5959.48 −0.514403
\(513\) 1624.05 2812.94i 0.139773 0.242094i
\(514\) −3028.11 + 5244.84i −0.259852 + 0.450078i
\(515\) −15468.3 −1.32352
\(516\) −846.066 + 1465.43i −0.0721821 + 0.125023i
\(517\) −12646.8 21905.0i −1.07584 1.86340i
\(518\) −711.639 1232.59i −0.0603622 0.104550i
\(519\) −2934.64 −0.248201
\(520\) 742.205 9346.33i 0.0625920 0.788200i
\(521\) 10858.8 0.913115 0.456558 0.889694i \(-0.349082\pi\)
0.456558 + 0.889694i \(0.349082\pi\)
\(522\) −1286.15 2227.67i −0.107841 0.186786i
\(523\) 5080.87 + 8800.33i 0.424801 + 0.735777i 0.996402 0.0847546i \(-0.0270106\pi\)
−0.571601 + 0.820532i \(0.693677\pi\)
\(524\) 2178.05 3772.48i 0.181581 0.314507i
\(525\) 2511.94 0.208819
\(526\) 4656.47 8065.23i 0.385992 0.668557i
\(527\) −772.482 + 1337.98i −0.0638517 + 0.110594i
\(528\) −2397.89 −0.197642
\(529\) −2457.36 + 4256.28i −0.201970 + 0.349821i
\(530\) −1099.58 1904.53i −0.0901184 0.156090i
\(531\) −1475.06 2554.89i −0.120551 0.208800i
\(532\) −21072.1 −1.71728
\(533\) 10234.1 4872.57i 0.831687 0.395975i
\(534\) 747.331 0.0605621
\(535\) 33.1620 + 57.4382i 0.00267984 + 0.00464162i
\(536\) 4479.07 + 7757.98i 0.360945 + 0.625175i
\(537\) 2779.41 4814.08i 0.223353 0.386858i
\(538\) −266.132 −0.0213267
\(539\) −12983.9 + 22488.7i −1.03758 + 1.79714i
\(540\) −778.019 + 1347.57i −0.0620012 + 0.107389i
\(541\) −9573.04 −0.760771 −0.380386 0.924828i \(-0.624209\pi\)
−0.380386 + 0.924828i \(0.624209\pi\)
\(542\) 2536.61 4393.54i 0.201027 0.348190i
\(543\) 1279.16 + 2215.58i 0.101094 + 0.175101i
\(544\) −4522.67 7833.49i −0.356448 0.617386i
\(545\) −5343.15 −0.419955
\(546\) −5572.89 + 2653.31i −0.436809 + 0.207969i
\(547\) 15958.9 1.24745 0.623724 0.781645i \(-0.285619\pi\)
0.623724 + 0.781645i \(0.285619\pi\)
\(548\) −649.898 1125.66i −0.0506611 0.0877475i
\(549\) 442.881 + 767.092i 0.0344293 + 0.0596333i
\(550\) −962.027 + 1666.28i −0.0745836 + 0.129183i
\(551\) −23452.0 −1.81323
\(552\) 3980.96 6895.23i 0.306958 0.531668i
\(553\) 2250.44 3897.88i 0.173053 0.299737i
\(554\) 9438.67 0.723846
\(555\) −479.105 + 829.835i −0.0366430 + 0.0634676i
\(556\) −2273.36 3937.58i −0.173403 0.300343i
\(557\) 1072.55 + 1857.70i 0.0815892 + 0.141317i 0.903933 0.427675i \(-0.140667\pi\)
−0.822344 + 0.568991i \(0.807334\pi\)
\(558\) 422.399 0.0320459
\(559\) 3722.33 + 2562.15i 0.281642 + 0.193859i
\(560\) 5023.47 0.379072
\(561\) −3397.07 5883.90i −0.255658 0.442813i
\(562\) −2180.28 3776.36i −0.163647 0.283445i
\(563\) 11159.3 19328.5i 0.835362 1.44689i −0.0583740 0.998295i \(-0.518592\pi\)
0.893736 0.448594i \(-0.148075\pi\)
\(564\) 9460.59 0.706317
\(565\) 7106.29 12308.5i 0.529140 0.916497i
\(566\) 2225.34 3854.40i 0.165261 0.286241i
\(567\) 2425.11 0.179621
\(568\) −3503.33 + 6067.95i −0.258797 + 0.448249i
\(569\) 9876.51 + 17106.6i 0.727671 + 1.26036i 0.957865 + 0.287218i \(0.0927304\pi\)
−0.230194 + 0.973145i \(0.573936\pi\)
\(570\) −2606.05 4513.80i −0.191500 0.331688i
\(571\) −10640.6 −0.779850 −0.389925 0.920847i \(-0.627499\pi\)
−0.389925 + 0.920847i \(0.627499\pi\)
\(572\) −1018.69 + 12828.0i −0.0744639 + 0.937699i
\(573\) −13323.9 −0.971401
\(574\) −5307.40 9192.69i −0.385935 0.668459i
\(575\) 1827.59 + 3165.47i 0.132549 + 0.229581i
\(576\) −623.318 + 1079.62i −0.0450895 + 0.0780974i
\(577\) 6547.89 0.472430 0.236215 0.971701i \(-0.424093\pi\)
0.236215 + 0.971701i \(0.424093\pi\)
\(578\) −1894.07 + 3280.62i −0.136302 + 0.236083i
\(579\) −3723.64 + 6449.54i −0.267270 + 0.462925i
\(580\) 11234.9 0.804319
\(581\) −5059.29 + 8762.94i −0.361264 + 0.625728i
\(582\) −471.061 815.902i −0.0335500 0.0581104i
\(583\) 3572.85 + 6188.35i 0.253812 + 0.439615i
\(584\) 15713.8 1.11343
\(585\) 3422.95 + 2356.09i 0.241917 + 0.166517i
\(586\) 2867.32 0.202130
\(587\) −2950.17 5109.84i −0.207439 0.359294i 0.743468 0.668771i \(-0.233179\pi\)
−0.950907 + 0.309477i \(0.899846\pi\)
\(588\) −4856.36 8411.46i −0.340600 0.589937i
\(589\) 1925.54 3335.14i 0.134704 0.233314i
\(590\) −4733.94 −0.330328
\(591\) 1890.35 3274.18i 0.131571 0.227888i
\(592\) 276.151 478.308i 0.0191719 0.0332067i
\(593\) −15261.5 −1.05686 −0.528428 0.848978i \(-0.677218\pi\)
−0.528428 + 0.848978i \(0.677218\pi\)
\(594\) −928.772 + 1608.68i −0.0641548 + 0.111119i
\(595\) 7116.70 + 12326.5i 0.490346 + 0.849305i
\(596\) 5202.00 + 9010.13i 0.357520 + 0.619243i
\(597\) 16562.9 1.13547
\(598\) −7398.23 5092.35i −0.505913 0.348230i
\(599\) −18900.6 −1.28925 −0.644623 0.764501i \(-0.722986\pi\)
−0.644623 + 0.764501i \(0.722986\pi\)
\(600\) −851.852 1475.45i −0.0579612 0.100392i
\(601\) 9253.48 + 16027.5i 0.628049 + 1.08781i 0.987943 + 0.154819i \(0.0494794\pi\)
−0.359894 + 0.932993i \(0.617187\pi\)
\(602\) 2115.91 3664.86i 0.143252 0.248120i
\(603\) −3970.36 −0.268135
\(604\) 3410.86 5907.79i 0.229778 0.397987i
\(605\) −4290.04 + 7430.56i −0.288289 + 0.499331i
\(606\) 7015.79 0.470292
\(607\) 3204.25 5549.92i 0.214261 0.371111i −0.738783 0.673944i \(-0.764599\pi\)
0.953044 + 0.302833i \(0.0979324\pi\)
\(608\) 11273.5 + 19526.3i 0.751976 + 1.30246i
\(609\) −8754.90 15163.9i −0.582539 1.00899i
\(610\) 1421.34 0.0943418
\(611\) 2000.01 25185.5i 0.132425 1.66759i
\(612\) 2541.21 0.167847
\(613\) 1753.63 + 3037.38i 0.115544 + 0.200128i 0.917997 0.396587i \(-0.129806\pi\)
−0.802453 + 0.596715i \(0.796472\pi\)
\(614\) −753.255 1304.68i −0.0495096 0.0857532i
\(615\) −3573.17 + 6188.91i −0.234283 + 0.405790i
\(616\) 28529.1 1.86602
\(617\) −7253.89 + 12564.1i −0.473307 + 0.819792i −0.999533 0.0305526i \(-0.990273\pi\)
0.526226 + 0.850345i \(0.323607\pi\)
\(618\) 3453.32 5981.33i 0.224778 0.389327i
\(619\) 4750.85 0.308486 0.154243 0.988033i \(-0.450706\pi\)
0.154243 + 0.988033i \(0.450706\pi\)
\(620\) −922.451 + 1597.73i −0.0597525 + 0.103494i
\(621\) 1764.41 + 3056.05i 0.114015 + 0.197480i
\(622\) 2496.49 + 4324.04i 0.160933 + 0.278743i
\(623\) 5087.14 0.327146
\(624\) −1972.95 1358.02i −0.126573 0.0871225i
\(625\) −11347.0 −0.726209
\(626\) 3528.32 + 6111.23i 0.225272 + 0.390182i
\(627\) 8467.76 + 14666.6i 0.539346 + 0.934175i
\(628\) 1514.20 2622.68i 0.0962154 0.166650i
\(629\) 1564.88 0.0991986
\(630\) 1945.73 3370.11i 0.123047 0.213124i
\(631\) −2412.60 + 4178.74i −0.152209 + 0.263634i −0.932039 0.362357i \(-0.881972\pi\)
0.779830 + 0.625991i \(0.215305\pi\)
\(632\) −3052.69 −0.192135
\(633\) −6791.69 + 11763.5i −0.426454 + 0.738640i
\(634\) 836.652 + 1449.12i 0.0524096 + 0.0907762i
\(635\) 12277.9 + 21266.0i 0.767298 + 1.32900i
\(636\) −2672.70 −0.166635
\(637\) −23419.2 + 11150.1i −1.45668 + 0.693539i
\(638\) 13411.9 0.832258
\(639\) −1552.72 2689.39i −0.0961262 0.166495i
\(640\) −6384.66 11058.6i −0.394337 0.683013i
\(641\) 2955.95 5119.85i 0.182142 0.315479i −0.760468 0.649376i \(-0.775030\pi\)
0.942610 + 0.333897i \(0.108364\pi\)
\(642\) −29.6139 −0.00182051
\(643\) −11704.1 + 20272.2i −0.717833 + 1.24332i 0.244024 + 0.969769i \(0.421532\pi\)
−0.961857 + 0.273554i \(0.911801\pi\)
\(644\) 11446.6 19826.2i 0.700405 1.21314i
\(645\) −2849.04 −0.173924
\(646\) −4256.01 + 7371.62i −0.259211 + 0.448967i
\(647\) 8199.33 + 14201.7i 0.498221 + 0.862944i 0.999998 0.00205298i \(-0.000653483\pi\)
−0.501777 + 0.864997i \(0.667320\pi\)
\(648\) −822.405 1424.45i −0.0498567 0.0863543i
\(649\) 15381.9 0.930342
\(650\) −1735.22 + 826.157i −0.104709 + 0.0498532i
\(651\) 2875.30 0.173106
\(652\) 1784.97 + 3091.65i 0.107216 + 0.185703i
\(653\) −13764.8 23841.3i −0.824897 1.42876i −0.901998 0.431741i \(-0.857900\pi\)
0.0771005 0.997023i \(-0.475434\pi\)
\(654\) 1192.87 2066.11i 0.0713224 0.123534i
\(655\) 7334.34 0.437521
\(656\) 2059.54 3567.22i 0.122578 0.212312i
\(657\) −3482.28 + 6031.48i −0.206783 + 0.358159i
\(658\) −23659.8 −1.40175
\(659\) 12089.9 20940.3i 0.714650 1.23781i −0.248444 0.968646i \(-0.579919\pi\)
0.963094 0.269164i \(-0.0867474\pi\)
\(660\) −4056.57 7026.19i −0.239245 0.414385i
\(661\) −2262.52 3918.80i −0.133134 0.230595i 0.791749 0.610847i \(-0.209171\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(662\) −11219.4 −0.658695
\(663\) 537.224 6765.08i 0.0314692 0.396281i
\(664\) 6862.84 0.401099
\(665\) −17739.6 30725.8i −1.03445 1.79172i
\(666\) −213.922 370.524i −0.0124464 0.0215578i
\(667\) 12739.4 22065.3i 0.739539 1.28092i
\(668\) −17452.2 −1.01085
\(669\) 6721.76 11642.4i 0.388458 0.672829i
\(670\) −3185.53 + 5517.49i −0.183683 + 0.318148i
\(671\) −4618.34 −0.265706
\(672\) −8417.05 + 14578.8i −0.483177 + 0.836887i
\(673\) −1643.59 2846.78i −0.0941393 0.163054i 0.815110 0.579307i \(-0.196677\pi\)
−0.909249 + 0.416253i \(0.863343\pi\)
\(674\) −1835.33 3178.89i −0.104888 0.181671i
\(675\) 755.102 0.0430576
\(676\) −8103.14 + 9977.74i −0.461035 + 0.567691i
\(677\) −9724.21 −0.552041 −0.276020 0.961152i \(-0.589016\pi\)
−0.276020 + 0.961152i \(0.589016\pi\)
\(678\) 3172.99 + 5495.77i 0.179731 + 0.311304i
\(679\) −3206.55 5553.91i −0.181231 0.313902i
\(680\) 4826.84 8360.34i 0.272207 0.471477i
\(681\) 17279.3 0.972309
\(682\) −1101.19 + 1907.31i −0.0618280 + 0.107089i
\(683\) −7274.33 + 12599.5i −0.407532 + 0.705867i −0.994613 0.103662i \(-0.966944\pi\)
0.587080 + 0.809529i \(0.300277\pi\)
\(684\) −6334.40 −0.354096
\(685\) 1094.23 1895.26i 0.0610342 0.105714i
\(686\) 4617.26 + 7997.33i 0.256979 + 0.445101i
\(687\) −6952.62 12042.3i −0.386112 0.668766i
\(688\) 1642.15 0.0909979
\(689\) −565.022 + 7115.13i −0.0312418 + 0.393418i
\(690\) 5662.54 0.312419
\(691\) −3364.48 5827.45i −0.185226 0.320820i 0.758427 0.651758i \(-0.225968\pi\)
−0.943653 + 0.330938i \(0.892635\pi\)
\(692\) 2861.54 + 4956.33i 0.157196 + 0.272271i
\(693\) −6322.22 + 10950.4i −0.346553 + 0.600248i
\(694\) −6591.76 −0.360548
\(695\) 3827.65 6629.69i 0.208908 0.361839i
\(696\) −5937.94 + 10284.8i −0.323387 + 0.560122i
\(697\) 11670.9 0.634241
\(698\) 2622.57 4542.43i 0.142215 0.246323i
\(699\) 8829.49 + 15293.1i 0.477771 + 0.827524i
\(700\) −2449.37 4242.43i −0.132254 0.229070i
\(701\) −29159.8 −1.57111 −0.785557 0.618789i \(-0.787624\pi\)
−0.785557 + 0.618789i \(0.787624\pi\)
\(702\) −1675.24 + 797.599i −0.0900682 + 0.0428824i
\(703\) −3900.73 −0.209273
\(704\) −3249.96 5629.10i −0.173988 0.301356i
\(705\) 7964.39 + 13794.7i 0.425470 + 0.736935i
\(706\) −5897.52 + 10214.8i −0.314385 + 0.544531i
\(707\) 47757.0 2.54044
\(708\) −2876.64 + 4982.50i −0.152699 + 0.264483i
\(709\) 10244.5 17744.0i 0.542653 0.939903i −0.456097 0.889930i \(-0.650753\pi\)
0.998751 0.0499730i \(-0.0159135\pi\)
\(710\) −4983.16 −0.263401
\(711\) 676.495 1171.72i 0.0356829 0.0618046i
\(712\) −1725.16 2988.06i −0.0908047 0.157278i
\(713\) 2091.96 + 3623.37i 0.109880 + 0.190318i
\(714\) −6355.26 −0.333109
\(715\) −19562.3 + 9313.83i −1.02320 + 0.487157i
\(716\) −10840.7 −0.565833
\(717\) 3203.77 + 5549.09i 0.166871 + 0.289030i
\(718\) −1592.85 2758.90i −0.0827919 0.143400i
\(719\) 8995.06 15579.9i 0.466563 0.808111i −0.532707 0.846300i \(-0.678825\pi\)
0.999271 + 0.0381883i \(0.0121587\pi\)
\(720\) 1510.08 0.0781631
\(721\) 23507.0 40715.3i 1.21421 2.10308i
\(722\) 5580.82 9666.26i 0.287668 0.498256i
\(723\) −14078.8 −0.724197
\(724\) 2494.60 4320.78i 0.128054 0.221796i
\(725\) −2726.00 4721.57i −0.139643 0.241869i
\(726\) −1915.52 3317.77i −0.0979222 0.169606i
\(727\) −37652.7 −1.92086 −0.960428 0.278528i \(-0.910153\pi\)
−0.960428 + 0.278528i \(0.910153\pi\)
\(728\) 23473.4 + 16157.2i 1.19503 + 0.822561i
\(729\) 729.000 0.0370370
\(730\) 5587.85 + 9678.45i 0.283309 + 0.490706i
\(731\) 2326.42 + 4029.48i 0.117710 + 0.203879i
\(732\) 863.698 1495.97i 0.0436109 0.0755364i
\(733\) 4524.26 0.227977 0.113989 0.993482i \(-0.463637\pi\)
0.113989 + 0.993482i \(0.463637\pi\)
\(734\) 5617.19 9729.26i 0.282472 0.489256i
\(735\) 8176.64 14162.4i 0.410340 0.710730i
\(736\) −24495.6 −1.22679
\(737\) 10350.7 17927.9i 0.517329 0.896040i
\(738\) −1595.43 2763.37i −0.0795781 0.137833i
\(739\) −409.151 708.671i −0.0203665 0.0352759i 0.855663 0.517534i \(-0.173150\pi\)
−0.876029 + 0.482258i \(0.839817\pi\)
\(740\) 1868.68 0.0928300
\(741\) −1339.12 + 16863.1i −0.0663885 + 0.836008i
\(742\) 6684.10 0.330702
\(743\) −19501.1 33776.9i −0.962888 1.66777i −0.715185 0.698935i \(-0.753658\pi\)
−0.247702 0.968836i \(-0.579676\pi\)
\(744\) −975.077 1688.88i −0.0480484 0.0832224i
\(745\) −8758.59 + 15170.3i −0.430725 + 0.746037i
\(746\) −15456.4 −0.758579
\(747\) −1520.85 + 2634.19i −0.0744912 + 0.129022i
\(748\) −6624.90 + 11474.7i −0.323838 + 0.560903i
\(749\) −201.584 −0.00983407
\(750\) 3313.70 5739.49i 0.161332 0.279435i
\(751\) 11188.8 + 19379.7i 0.543658 + 0.941643i 0.998690 + 0.0511678i \(0.0162943\pi\)
−0.455032 + 0.890475i \(0.650372\pi\)
\(752\) −4590.59 7951.13i −0.222608 0.385569i
\(753\) 11708.6 0.566649
\(754\) 11035.1 + 7595.67i 0.532990 + 0.366868i
\(755\) 11485.7 0.553653
\(756\) −2364.70 4095.78i −0.113761 0.197040i
\(757\) 17256.3 + 29888.8i 0.828521 + 1.43504i 0.899198 + 0.437542i \(0.144151\pi\)
−0.0706770 + 0.997499i \(0.522516\pi\)
\(758\) 4013.85 6952.19i 0.192335 0.333133i
\(759\) −18399.2 −0.879905
\(760\) −12031.7 + 20839.5i −0.574258 + 0.994645i
\(761\) −9987.78 + 17299.3i −0.475764 + 0.824048i −0.999615 0.0277624i \(-0.991162\pi\)
0.523850 + 0.851810i \(0.324495\pi\)
\(762\) −10964.3 −0.521251
\(763\) 8119.95 14064.2i 0.385271 0.667309i
\(764\) 12992.0 + 22502.8i 0.615228 + 1.06561i
\(765\) 2139.32 + 3705.40i 0.101107 + 0.175123i
\(766\) −1184.73 −0.0558827
\(767\) 12656.0 + 8711.38i 0.595804 + 0.410104i
\(768\) 9025.91 0.424081
\(769\) 16532.4 + 28635.0i 0.775260 + 1.34279i 0.934648 + 0.355574i \(0.115715\pi\)
−0.159388 + 0.987216i \(0.550952\pi\)
\(770\) 10145.0 + 17571.6i 0.474805 + 0.822387i
\(771\) −6196.25 + 10732.2i −0.289432 + 0.501312i
\(772\) 14523.6 0.677091
\(773\) 9282.01 16076.9i 0.431890 0.748055i −0.565146 0.824991i \(-0.691180\pi\)
0.997036 + 0.0769359i \(0.0245137\pi\)
\(774\) 636.052 1101.68i 0.0295380 0.0511614i
\(775\) 895.279 0.0414960
\(776\) −2174.82 + 3766.90i −0.100608 + 0.174257i
\(777\) −1456.19 2522.19i −0.0672334 0.116452i
\(778\) −5175.53 8964.28i −0.238498 0.413091i
\(779\) −29091.6 −1.33802
\(780\) 641.520 8078.45i 0.0294489 0.370840i
\(781\) 16191.7 0.741848
\(782\) −4623.83 8008.71i −0.211442 0.366229i
\(783\) −2631.77 4558.36i −0.120117 0.208049i
\(784\) −4712.93 + 8163.04i −0.214693 + 0.371858i
\(785\) 5098.91 0.231832
\(786\) −1637.40 + 2836.07i −0.0743057 + 0.128701i
\(787\) −18218.4 + 31555.2i −0.825179 + 1.42925i 0.0766032 + 0.997062i \(0.475593\pi\)
−0.901782 + 0.432190i \(0.857741\pi\)
\(788\) −7373.04 −0.333317
\(789\) 9528.26 16503.4i 0.429930 0.744661i
\(790\) −1085.54 1880.21i −0.0488884 0.0846772i
\(791\) 21598.8 + 37410.2i 0.970877 + 1.68161i
\(792\) 8576.00 0.384766
\(793\) −3799.90 2615.55i −0.170162 0.117126i
\(794\) 2081.71 0.0930441
\(795\) −2250.01 3897.13i −0.100377 0.173858i
\(796\) −16150.3 27973.2i −0.719137 1.24558i
\(797\) −6182.80 + 10708.9i −0.274788 + 0.475947i −0.970082 0.242779i \(-0.921941\pi\)
0.695294 + 0.718726i \(0.255274\pi\)
\(798\) 15841.6 0.702738
\(799\) 13006.9 22528.6i 0.575907 0.997501i
\(800\) −2620.80 + 4539.37i −0.115824 + 0.200614i
\(801\) 1529.22 0.0674561
\(802\) 7822.19 13548.4i 0.344403 0.596523i
\(803\) −18156.5 31448.0i −0.797918 1.38204i
\(804\) 3871.46 + 6705.56i 0.169821 + 0.294138i
\(805\) 38545.4 1.68763
\(806\) −1986.23 + 945.665i −0.0868015 + 0.0413271i
\(807\) −544.571 −0.0237544
\(808\) −16195.4 28051.3i −0.705140 1.22134i
\(809\) 4046.87 + 7009.39i 0.175872 + 0.304619i 0.940463 0.339897i \(-0.110392\pi\)
−0.764591 + 0.644516i \(0.777059\pi\)
\(810\) 584.897 1013.07i 0.0253718 0.0439453i
\(811\) 15984.7 0.692105 0.346052 0.938215i \(-0.387522\pi\)
0.346052 + 0.938215i \(0.387522\pi\)
\(812\) −17073.6 + 29572.4i −0.737891 + 1.27806i
\(813\) 5190.53 8990.26i 0.223911 0.387825i
\(814\) 2230.77 0.0960546
\(815\) −3005.34 + 5205.40i −0.129169 + 0.223727i
\(816\) −1233.08 2135.76i −0.0529000 0.0916255i
\(817\) −5798.99 10044.2i −0.248325 0.430111i
\(818\) −9312.03 −0.398029
\(819\) −11403.5 + 5429.32i −0.486533 + 0.231643i
\(820\) 13936.6 0.593523
\(821\) 13430.9 + 23263.1i 0.570942 + 0.988900i 0.996470 + 0.0839550i \(0.0267552\pi\)
−0.425528 + 0.904945i \(0.639911\pi\)
\(822\) 488.578 + 846.242i 0.0207313 + 0.0359076i
\(823\) 2602.97 4508.48i 0.110248 0.190955i −0.805622 0.592429i \(-0.798169\pi\)
0.915870 + 0.401475i \(0.131502\pi\)
\(824\) −31886.9 −1.34810
\(825\) −1968.54 + 3409.61i −0.0830737 + 0.143888i
\(826\) 7194.14 12460.6i 0.303046 0.524891i
\(827\) 46621.5 1.96032 0.980162 0.198200i \(-0.0635095\pi\)
0.980162 + 0.198200i \(0.0635095\pi\)
\(828\) 3440.92 5959.85i 0.144421 0.250144i
\(829\) 20914.9 + 36225.6i 0.876241 + 1.51769i 0.855435 + 0.517910i \(0.173290\pi\)
0.0208053 + 0.999784i \(0.493377\pi\)
\(830\) 2440.44 + 4226.96i 0.102059 + 0.176771i
\(831\) 19313.8 0.806244
\(832\) 513.960 6472.12i 0.0214163 0.269688i
\(833\) −26707.0 −1.11086
\(834\) 1709.06 + 2960.18i 0.0709592 + 0.122905i
\(835\) −14692.1 25447.5i −0.608913 1.05467i
\(836\) 16513.7 28602.5i 0.683179 1.18330i
\(837\) 864.331 0.0356937
\(838\) 4118.19 7132.91i 0.169762 0.294036i
\(839\) −6342.54 + 10985.6i −0.260988 + 0.452044i −0.966505 0.256649i \(-0.917382\pi\)
0.705517 + 0.708693i \(0.250715\pi\)
\(840\) −17966.3 −0.737972
\(841\) −6807.43 + 11790.8i −0.279119 + 0.483448i
\(842\) −1112.99 1927.75i −0.0455535 0.0789009i
\(843\) −4461.39 7727.35i −0.182276 0.315711i
\(844\) 26490.1 1.08036
\(845\) −21370.4 3415.64i −0.870017 0.139055i
\(846\) −7112.25 −0.289036
\(847\) −13039.1 22584.3i −0.528959 0.916183i
\(848\) 1296.88 + 2246.27i 0.0525179 + 0.0909636i
\(849\) 4553.58 7887.03i 0.184074 0.318825i
\(850\) −1978.83 −0.0798509
\(851\) 2118.92 3670.08i 0.0853534 0.147836i
\(852\) −3028.08 + 5244.80i −0.121761 + 0.210896i
\(853\) −37493.3 −1.50498 −0.752488 0.658606i \(-0.771146\pi\)
−0.752488 + 0.658606i \(0.771146\pi\)
\(854\) −2160.00 + 3741.24i −0.0865501 + 0.149909i
\(855\) −5332.60 9236.34i −0.213300 0.369446i
\(856\) 68.3614 + 118.405i 0.00272961 + 0.00472782i
\(857\) −11826.3 −0.471386 −0.235693 0.971828i \(-0.575736\pi\)
−0.235693 + 0.971828i \(0.575736\pi\)
\(858\) 765.824 9643.76i 0.0304718 0.383721i
\(859\) −36498.7 −1.44973 −0.724866 0.688890i \(-0.758099\pi\)
−0.724866 + 0.688890i \(0.758099\pi\)
\(860\) 2778.07 + 4811.76i 0.110153 + 0.190790i
\(861\) −10860.2 18810.5i −0.429867 0.744552i
\(862\) −3643.36 + 6310.48i −0.143960 + 0.249346i
\(863\) 2292.79 0.0904372 0.0452186 0.998977i \(-0.485602\pi\)
0.0452186 + 0.998977i \(0.485602\pi\)
\(864\) −2530.21 + 4382.45i −0.0996290 + 0.172563i
\(865\) −4817.96 + 8344.95i −0.189382 + 0.328020i
\(866\) 4836.24 0.189772
\(867\) −3875.72 + 6712.95i −0.151818 + 0.262957i
\(868\) −2803.68 4856.12i −0.109635 0.189893i
\(869\) 3527.22 + 6109.33i 0.137690 + 0.238487i
\(870\) −8446.16 −0.329140
\(871\) 18669.6 8888.81i 0.726288 0.345793i
\(872\) −11014.6 −0.427753
\(873\) −963.906 1669.53i −0.0373691 0.0647253i
\(874\) 11525.7 + 19963.1i 0.446066 + 0.772609i
\(875\) 22556.6 39069.2i 0.871488 1.50946i
\(876\) 13582.1 0.523856
\(877\) 10400.1 18013.6i 0.400442 0.693587i −0.593337 0.804954i \(-0.702190\pi\)
0.993779 + 0.111368i \(0.0355231\pi\)
\(878\) −4433.84 + 7679.63i −0.170427 + 0.295188i
\(879\) 5867.23 0.225139
\(880\) −3936.76 + 6818.67i −0.150805 + 0.261202i
\(881\) 9627.95 + 16676.1i 0.368188 + 0.637721i 0.989282 0.146015i \(-0.0466448\pi\)
−0.621094 + 0.783736i \(0.713311\pi\)
\(882\) 3650.90 + 6323.54i 0.139379 + 0.241411i
\(883\) 1744.49 0.0664857 0.0332429 0.999447i \(-0.489417\pi\)
0.0332429 + 0.999447i \(0.489417\pi\)
\(884\) −11949.4 + 5689.25i −0.454642 + 0.216460i
\(885\) −9686.80 −0.367930
\(886\) 5001.33 + 8662.56i 0.189642 + 0.328470i
\(887\) −1485.35 2572.70i −0.0562268 0.0973877i 0.836542 0.547903i \(-0.184574\pi\)
−0.892769 + 0.450515i \(0.851240\pi\)
\(888\) −987.647 + 1710.65i −0.0373235 + 0.0646462i
\(889\) −74634.6 −2.81571
\(890\) 1226.94 2125.11i 0.0462101 0.0800382i
\(891\) −1900.49 + 3291.75i −0.0714578 + 0.123769i
\(892\) −26217.3 −0.984104
\(893\) −32421.8 + 56156.2i −1.21495 + 2.10436i
\(894\) −3910.74 6773.60i −0.146303 0.253404i
\(895\) −9126.24 15807.1i −0.340845 0.590361i
\(896\) 38810.9 1.44708
\(897\) −15138.6 10420.2i −0.563503 0.387871i
\(898\) −601.703 −0.0223598
\(899\) −3120.33 5404.57i −0.115761 0.200503i
\(900\) −736.293 1275.30i −0.0272701 0.0472332i
\(901\) −3674.56 + 6364.52i −0.135868 + 0.235331i
\(902\) 16637.1 0.614140
\(903\) 4329.66 7499.19i 0.159559 0.276365i
\(904\) 14649.2 25373.2i 0.538966 0.933516i
\(905\) 8400.32 0.308548
\(906\) −2564.21 + 4441.34i −0.0940288 + 0.162863i
\(907\) −16501.7 28581.7i −0.604111 1.04635i −0.992191 0.124726i \(-0.960195\pi\)
0.388080 0.921626i \(-0.373138\pi\)
\(908\) −16848.8 29183.1i −0.615802 1.06660i
\(909\) 14356.0 0.523827
\(910\) −1604.36 + 20203.2i −0.0584441 + 0.735967i
\(911\) 14977.0 0.544686 0.272343 0.962200i \(-0.412201\pi\)
0.272343 + 0.962200i \(0.412201\pi\)
\(912\) 3073.66 + 5323.73i 0.111600 + 0.193296i
\(913\) −7929.66 13734.6i −0.287441 0.497862i
\(914\) −12200.0 + 21131.1i −0.441511 + 0.764720i
\(915\) 2908.41 0.105081
\(916\) −13558.9 + 23484.7i −0.489080 + 0.847112i
\(917\) −11145.9 + 19305.3i −0.401386 + 0.695221i
\(918\) −1910.42 −0.0686856
\(919\) −5712.69 + 9894.67i −0.205054 + 0.355163i −0.950150 0.311794i \(-0.899070\pi\)
0.745096 + 0.666957i \(0.232404\pi\)
\(920\) −13071.6 22640.6i −0.468431 0.811346i
\(921\) −1541.34 2669.68i −0.0551455 0.0955147i
\(922\) 17196.9 0.614263
\(923\) 13322.3 + 9169.99i 0.475090 + 0.327014i
\(924\) 24659.0 0.877944
\(925\) −453.410 785.329i −0.0161168 0.0279151i
\(926\) −2613.27 4526.32i −0.0927403 0.160631i
\(927\) 7066.33 12239.2i 0.250365 0.433646i
\(928\) 36537.3 1.29245
\(929\) −5977.10 + 10352.6i −0.211090 + 0.365618i −0.952056 0.305924i \(-0.901035\pi\)
0.740966 + 0.671542i \(0.234368\pi\)
\(930\) 693.477 1201.14i 0.0244516 0.0423515i
\(931\) 66571.7 2.34350
\(932\) 17219.1 29824.4i 0.605183 1.04821i
\(933\) 5108.42 + 8848.04i 0.179252 + 0.310474i
\(934\) 831.870 + 1440.84i 0.0291431 + 0.0504773i
\(935\) −22308.7 −0.780290
\(936\) 7056.21 + 4856.93i 0.246410 + 0.169609i
\(937\) 42546.4 1.48338 0.741692 0.670740i \(-0.234024\pi\)
0.741692 + 0.670740i \(0.234024\pi\)
\(938\) −9682.04 16769.8i −0.337025 0.583745i
\(939\) 7219.81 + 12505.1i 0.250915 + 0.434598i
\(940\) 15532.0 26902.2i 0.538934 0.933461i
\(941\) 20665.1 0.715903 0.357951 0.933740i \(-0.383475\pi\)
0.357951 + 0.933740i \(0.383475\pi\)
\(942\) −1138.34 + 1971.67i −0.0393728 + 0.0681957i
\(943\) 15802.9 27371.5i 0.545720 0.945215i
\(944\) 5583.37 0.192503
\(945\) 3981.44 6896.06i 0.137054 0.237385i
\(946\) 3316.36 + 5744.10i 0.113979 + 0.197417i
\(947\) 4746.87 + 8221.81i 0.162885 + 0.282126i 0.935902 0.352260i \(-0.114587\pi\)
−0.773017 + 0.634385i \(0.781253\pi\)
\(948\) −2638.58 −0.0903976
\(949\) 2871.33 36157.7i 0.0982163 1.23681i
\(950\) 4932.56 0.168456
\(951\) 1711.99 + 2965.26i 0.0583756 + 0.101110i
\(952\) 14670.6 + 25410.3i 0.499452 + 0.865076i
\(953\) −26667.1 + 46188.7i −0.906433 + 1.56999i −0.0874512 + 0.996169i \(0.527872\pi\)
−0.818982 + 0.573819i \(0.805461\pi\)
\(954\) 2009.28 0.0681894
\(955\) −21874.6 + 37887.9i −0.741199 + 1.28379i
\(956\) 6247.93 10821.7i 0.211373 0.366108i
\(957\) 27443.9 0.926997
\(958\) −14201.1 + 24597.0i −0.478932 + 0.829534i
\(959\) 3325.79 + 5760.44i 0.111987 + 0.193967i
\(960\) 2046.67 + 3544.94i 0.0688084 + 0.119180i
\(961\) −28766.2 −0.965601
\(962\) 1835.45 + 1263.37i 0.0615147 + 0.0423418i
\(963\) −60.5972 −0.00202774
\(964\) 13728.1 + 23777.7i 0.458663 + 0.794428i
\(965\) 12226.6 + 21177.2i 0.407865 + 0.706443i
\(966\) −8605.32 + 14904.9i −0.286617 + 0.496435i
\(967\) −42110.1 −1.40038 −0.700191 0.713956i \(-0.746902\pi\)
−0.700191 + 0.713956i \(0.746902\pi\)
\(968\) −8843.65 + 15317.7i −0.293642 + 0.508604i
\(969\) −8708.83 + 15084.1i −0.288718 + 0.500074i
\(970\) −3093.47 −0.102397
\(971\) 6913.86 11975.2i 0.228503 0.395779i −0.728862 0.684661i \(-0.759950\pi\)
0.957365 + 0.288882i \(0.0932836\pi\)
\(972\) −710.841 1231.21i −0.0234570 0.0406288i
\(973\) 11633.7 + 20150.2i 0.383309 + 0.663911i
\(974\) 13262.3 0.436295
\(975\) −3550.69 + 1690.52i −0.116629 + 0.0555281i
\(976\) −1676.38 −0.0549791
\(977\) −566.943 981.973i −0.0185651 0.0321557i 0.856594 0.515992i \(-0.172576\pi\)
−0.875159 + 0.483836i \(0.839243\pi\)
\(978\) −1341.90 2324.23i −0.0438743 0.0759926i
\(979\) −3986.65 + 6905.09i −0.130147 + 0.225421i
\(980\) −31891.9 −1.03954
\(981\) 2440.90 4227.76i 0.0794413 0.137596i
\(982\) 10558.4 18287.6i 0.343107 0.594279i
\(983\) 26250.2 0.851729 0.425865 0.904787i \(-0.359970\pi\)
0.425865 + 0.904787i \(0.359970\pi\)
\(984\) −7365.87 + 12758.1i −0.238633 + 0.413325i
\(985\) −6206.98 10750.8i −0.200783 0.347766i
\(986\) 6896.84 + 11945.7i 0.222759 + 0.385829i
\(987\) −48413.7 −1.56132
\(988\) 29786.0 14181.4i 0.959128 0.456651i
\(989\) 12600.3 0.405124
\(990\) 3049.64 + 5282.13i 0.0979028 + 0.169573i
\(991\) 14680.2 + 25426.8i 0.470566 + 0.815045i 0.999433 0.0336599i \(-0.0107163\pi\)
−0.528867 + 0.848705i \(0.677383\pi\)
\(992\) −2999.92 + 5196.01i −0.0960156 + 0.166304i
\(993\) −22957.7 −0.733676
\(994\) 7572.87 13116.6i 0.241647 0.418544i
\(995\) 27192.3 47098.4i 0.866384 1.50062i
\(996\) 5931.86 0.188713
\(997\) −8417.95 + 14580.3i −0.267401 + 0.463153i −0.968190 0.250216i \(-0.919498\pi\)
0.700789 + 0.713369i \(0.252832\pi\)
\(998\) −6831.85 11833.1i −0.216692 0.375321i
\(999\) −437.737 758.182i −0.0138632 0.0240118i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 39.4.e.c.16.3 8
3.2 odd 2 117.4.g.e.55.2 8
4.3 odd 2 624.4.q.i.289.4 8
13.2 odd 12 507.4.b.h.337.5 8
13.3 even 3 507.4.a.m.1.2 4
13.9 even 3 inner 39.4.e.c.22.3 yes 8
13.10 even 6 507.4.a.i.1.3 4
13.11 odd 12 507.4.b.h.337.4 8
39.23 odd 6 1521.4.a.bb.1.2 4
39.29 odd 6 1521.4.a.v.1.3 4
39.35 odd 6 117.4.g.e.100.2 8
52.35 odd 6 624.4.q.i.529.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.c.16.3 8 1.1 even 1 trivial
39.4.e.c.22.3 yes 8 13.9 even 3 inner
117.4.g.e.55.2 8 3.2 odd 2
117.4.g.e.100.2 8 39.35 odd 6
507.4.a.i.1.3 4 13.10 even 6
507.4.a.m.1.2 4 13.3 even 3
507.4.b.h.337.4 8 13.11 odd 12
507.4.b.h.337.5 8 13.2 odd 12
624.4.q.i.289.4 8 4.3 odd 2
624.4.q.i.529.4 8 52.35 odd 6
1521.4.a.v.1.3 4 39.29 odd 6
1521.4.a.bb.1.2 4 39.23 odd 6